Two white dwarfs with a total mass $>1.4\:M_{\odot}$ merge. It may trigger a type Ia SN explosion.
How about the three cases below?
Two low mass WDs merge, total mass $<1.4\:M_{\odot}$.
A low mass WD + a low mass neutron star, total mass $<2\:M_{\odot}$ but $>1.4\:M_{\odot}$.
A low mass WD + a neutron star, total mass $>2\:M_{\odot}$.
If any of the above can result in a SN, have we observed this kind of SN?
I don't think any of those would give a supernova, because the first two don't cross an important mass boundary, and the last one might make a black hole from a neutron star, but that's not going to be much of a supernova because it's already very compact and there's not going to be much to have a core bounce off of, nor is the white dwarf massive enough for a type Ia. They should all produce some significant emission, depending on how fast the mass is introduced. Perhaps somewhere between what we would call a supernova, and something more along the lines of a classical nova (for the first one) and quasiperiodic X-ray flaring (for the next two). They could get pretty bright, and I don't know if the nomenclature has individual names for each one of those, but they don't quite sound like supernovae.
